Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics.

In mathematics a combination is a way of selecting several things out of a larger group, where ( unlike permutations ) order does not matter.

* The The Nine Chapters on the Mathematical Art, a mathematics Chinese book composed by several generations scholars of Han Dynasty.

Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes.

Fermi's interest in physics was further encouraged by Adolfo Amidei, a friend of his father, who gave him several books on physics and mathematics, which he read and assimilated quickly.

In mathematics, especially in category theory and homotopy theory, a groupoid ( less often Brandt groupoid or virtual group ) generalises the notion of group in several equivalent ways.

In mathematics, the harmonic mean ( sometimes called the subcontrary mean ) is one of several kinds of average.

In mathematics, the inverse limit ( also called the projective limit ) is a construction which allows one to " glue together " several related objects, the precise manner of the gluing process being specified by morphisms between the objects.

He had several interests outside his work, including archaeology and mathematics.

He left academia several times: serving as an officer on the frontline during World War I, where he was decorated a number of times for his courage ; teaching in schools in remote Austrian villages, where he encountered controversy for hitting children when they made mistakes in mathematics ; and working during World War II as a hospital porter in London, where he told patients not to take the drugs they were prescribed, and where no-one knew he was one of the world's most famous philosophers.

The American Mathematical Society and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

Monoids occur in several branches of mathematics ; for instance, they can be regarded as categories with a single object.

* Null ( mathematics ), a zero value in several branches of mathematics

After his father's death in 1901 Spengler attended several universities ( Munich, Berlin, and Halle ) as a private scholar, taking courses in a wide range of subjects: history, philosophy, mathematics, natural science, literature, the classics, music, and fine arts.

In mathematics, it is possible to combine several rings into one large product ring.

He or she will usually have a primary qualification in one of several fields: mathematics, the physical sciences ( e. g. chemistry, physics, biology ), engineering ( e. g. mechanical, chemical, Materials Science & Engineering or civil engineering ), medicine, or certain technologies, notably materials or food.

* Malba Tahan, pseudonym of Júlio César de Mello e Souza, author of several books figuring recreational mathematics, including The Man Who Counted

" Transformation " has several ( not always related ) meanings in various fields of mathematics.

The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

In any of several studies that treat the use of signs-for example, in linguistics, logic, mathematics, semantics, and semiotics-the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.

In mathematics, logic, and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general.

In pure and applied mathematics, he produced many results, proved many theorems, and proposed several conjectures.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

For example, in formal languages like mathematics, a ' stipulative ' definition guides a specific discussion.

In mathematics, the discrete Fourier transform ( DFT ) is a specific kind of discrete transform, used in Fourier analysis.

The degree generally includes units covering physics, mathematics, computer science, project management and specific topics in electrical engineering.

There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory ; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.

Kronecker, now seen as one of the founders of the constructive viewpoint in mathematics, disliked much of Cantor's set theory because it asserted the existence of sets satisfying certain properties, without giving specific examples of sets whose members did indeed satisfy those properties.

In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines ( e. g. Fuzzy Sets and Systems ), intuitionist mathematics is more rigorous than conventionally founded mathematics, where, ironically, the foundational elements which Intuitionism attempts to construct / refute / refound are taken as intuitively given.

However, Pythagoras believed that the mathematics of music should be based on the specific ratio of 3: 2 whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves.

In specific disciplines, Stanford was ranked in English ( in the United States ), in modern languages ( 7 ), in history ( 8 ), in philosophy ( 4 ), in geography & area studies ( 4 ), in linguistics ( 3 ), in computer science ( 2 ), in civil & structural engineering ( 2 ), in chemical engineering ( 3 ), in electrical engineering ( 2 ), in mechanical, aeronautical, & manufacturing engineering, in medicine ( 3 ), in biological sciences ( 3 ), in chemistry ( 4 ), in physics and astronomy ( 4 ), in metallurgy ( 4 ), in mathematics ( 3 ), in environmental sciences ( 4 ), in earth and marine sciences ( 6 ), in psychology ( 2 ), in sociology ( 4 ), in statistics, in politics and international studies ( 4 ), in law ( 3 ), in economics ( 3 ), and in account and finance.

Non-computational questions are generally math history or involve a specific aspect of mathematics, and are similar to the other subject areas.

In mathematics, " complete " is a term that takes on specific meanings in specific situations, and not every situation in which a type of " completion " occurs is called a " completion ".

Both Spinoza and Leibniz asserted that, in principle, all knowledge, including scientific knowledge, could be gained through the use of reason alone, though they both observed that this was not possible in practice for human beings except in specific areas such as mathematics.

In what is, in the U. S., called traditional mathematics, a specific process is taught to students at the end of the 1st year or during the 2nd year for use with multi-digit whole numbers, and is extended in either the fourth or fifth grade to include decimal representations of fractional numbers.

In mathematics the term additive function has two different definitions, depending on the specific field of application.

Some schools were a type of specialized school with a specific focus in a particular field or fields such as mathematics, physics, language, science, sports, etc.

Some Greek astronomers ( e. g., Aristarchus of Samos ) speculated that the planets ( Earth included ) orbited the Sun, but the optics ( and the specific mathematics – Newton's Law of Gravitation for example ) necessary to provide data that would convincingly support the heliocentric model did not exist in Ptolemy's time and would not come around for over fifteen hundred years after his death.

In financial mathematics and financial risk management, Value at Risk ( VaR ) is a widely used risk measure of the risk of loss on a specific portfolio of financial assets.

Beta is often used to denote a variable in mathematics and physics, where it often has specific meanings for certain applications, such as representing beta radiation.

In some cases the student's bachelor's degree must be in the same subject as the intended master's degree ( e. g. a Master of Economics will typically require a Bachelors with a major in economics ), or in a closely allied, " cognate ", discipline ( e. g. Applied Mathematics degrees may accept graduates in physics, mathematics or computer science ); in others, the subject of the bachelor's degree is unimportant ( e. g. MBA ) although, often in these cases, undergraduate coursework in specific subjects may be required ( e. g. some M. S. F.

In mathematics, an open sentence ( usually an equation or equality ) is described as " open " in the sense that its truth value is meaningless until its variables are replaced with specific numbers, at which point the truth value can usually be determined ( and hence the sentences are no longer regarded as " open ").